Question: The grades on a language midterm at Loyola are normally distributed with $\mu = 83$ and $\sigma = 4.5$. Jessica earned a $75$ on the exam. Find the z-score for Jessica's exam grade. Round to two decimal places.
Answer: A z-score is defined as the number of standard deviations a specific point is away from the mean We can calculate the z-score for Jessica's exam grade by subtracting the mean $(\mu)$ from her grade and then dividing by the standard deviation $(\sigma)$ $ { z = \dfrac{x - {\mu}}{{\sigma}}} $ $ { z = \dfrac{75 - {83}}{{4.5}}} $ ${ z \approx -1.78}$ The z-score is $-1.78$. In other words, Jessica's score was $1.78$ standard deviations below the mean.